Abstract
This paper is concerned with the time-step condition of commonly-used linearized semi-implicit schemes for nonlinear parabolic PDEs with Galerkin finite element approximations. In particular, we study the time-dependent nonlinear Joule heating equations. We present optimal error estimates of the semi-implicit Euler scheme in both the L2 norm and the H1 norm without any time-step restriction. Theoretical analysis is based on a new splitting of error function and precise analysis of a corresponding time-discrete system. The method used in this paper is appli- cable for more general nonlinear parabolic systems and many other linearized (semi)-implicit time discretizations for which previous works often require certain restriction on the time-step size τ.
Original language | English |
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Pages (from-to) | 622-633 |
Number of pages | 12 |
Journal | International Journal of Numerical Analysis and Modeling |
Volume | 10 |
Issue number | 3 |
Publication status | Published - 14 Jun 2013 |
Externally published | Yes |
Keywords
- Galerkin method
- Linearized semi- implicit scheme
- Nonlinear parabolic system
- Unconditionally optimal error estimate
ASJC Scopus subject areas
- Numerical Analysis